Optimal production control of a failure-prone machine

Optimal production control of a failure-prone machine

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Article ID: iaor20108883
Volume: 182
Issue: 1
Start Page Number: 67
End Page Number: 86
Publication Date: Jan 2011
Journal: Annals of Operations Research
Authors: , ,
Keywords: optimization
Abstract:

We consider a problem of optimal production control of a single unreliable machine. The objective is to minimize a discounted convex inventory/backlog cost over an infinite horizon. Using the variational analysis methodology, we develop the necessary conditions of optimality in terms of the co-state dynamics. We show that an inventory-threshold control policy is optimal when the work and repair times are exponentially distributed, and demonstrate how to find the value of the threshold in this case. We consider also a class of distributions concentrated on finite intervals and prove properties of the optimal trajectories, as well as properties of an optimal inventory threshold that is time dependent in this case.

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